Question

The following expression is the area of a rectangle. Find the possible length and breadth of the rectangle.

x² – 6x + 8

Answer 1

Given, area of a rectangle = x² – 6x + 8

Now, we have to find the possible length and breadth of the rectangle.

So, we factorise the given expression.

i.e. x² – 6x + 8 = x² – (4 + 2)x + 8

= x² – 4x – 2x + 8

= x(x – 4) – 2(x – 4)

= (x – 4)(x – 2)

Since, area of a rectangle = Length × Breadth.

Hence, the possible length and breadth are (x – 4) and (x – 2).